Design of IIR Digital Differentiators Using Constrained Optimization

A new optimization method for the design of fullband and lowpass IIR digital differentiators is proposed. In the new method, the passband phase-response error is minimized under the constraint that the maximum passband amplitude-response relative error is below a prescribed level. For lowpass IIR differentiators, an additional constraint is introduced to limit the average squared amplitude response in the stopband so as to minimize any high-frequency noise that may be present. Extensive experimental results are included, which show that the differentiators designed using the proposed method have much smaller maximum phase-response error for the same passband amplitude-response error and stopband constraints when compared with several differentiators designed using state-of-the-art competing methods.